We establish an isomorphism between the center Endℋ'(1) of the Heisenberg category defined by Khovanov in [13] and the algebra Λ* of shifted symmetric functions defined by Okounkov–Olshanski in [18]. We give a graphical description of the shifted power and Schur bases of Λ* as elements of Endℋ'(1), and describe the curl generators of Endℋ'(1) in the language of shifted symmetric functions. This latter description makes use of the transition and co-transition measures of Kerov [10] and the noncommutative probability spaces of Biane [2]